The Water Poverty Index (WPI) was created as an interdisciplinary indicator to assess water stress and scarcity, linking physical estimates of water availability with the socioeconomic drivers of poverty. This index has found great relevance in policy making as an effective water management tool, particularly in resources allocation and prioritization processes. Two conceptual weaknesses exist in the current index: (1) inadequate technique to combine available data and (2) poor statistical properties of the resulting composite. The purpose of this paper is to propose a suitable methodology to assess water poverty that overcomes these weaknesses. To this end, a number of combinations to create the WPI have been considered, based on indicators selection criteria, simple aggregation functions and multivariate analysis. The approach adopted has been designed for universal application at local scale. To exemplify the utilization of each alternative method, they have been piloted and implemented in the Turkana ...

A very simple and general expression of the consistent tangent matrix for substepping time-integration schemes is presented. If needed, the derivatives required for the computation of the consistent tangent moduli can be obtained via numerical differentiation. These two strategies (substepping and numerical differentiation) lead to quadratic convergence in complex nonlinear inelasticity problems.

We present in this paper the characterization of the variational structure behind the discrete equations defining the closest‐point projection approximation in elastoplasticity. Rate‐independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range, the later in the context of isotropic finite‐strain multiplicative plasticity. Primal variational principles in terms of the stresses and stress‐like hardening variables are presented first, followed by the formulation of dual principles incorporating explicitly the plastic multiplier. Augmented Lagrangian extensions are also presented allowing a complete regularization of the problem in the constrained rate‐independent limit. The variational structure identified in this paper leads to the proper framework for the development of new improved numerical algorithms for the integration of the local constitutive equations of plasticity as it is undertaken in Part II of this work. Copyright © 2001 John Wiley & Sons, Ltd.

In this paper, numerical differentiation is applied to integrate plastic constitutive laws and to compute the corresponding consistent tangent operators. The derivatives of the constitutive equations are approximated by means of difference schemes. These derivatives are needed to achieve quadratic convergence in the integration at Gauss-point level and in the solution of the boundary value problem. Numerical differentiation is shown to be a simple, robust and competitive alternative to analytical derivatives. Quadratic convergence is maintained, provided that adequate schemes and stepsizes are chosen. This point is illustrated by means of some numerical examples.Peer ReviewedPostprint (author’s final draft